We know standard deviation quantifies the spread of data from the mean. It is an absolute measure, and therefore, it has the same unit as the variable. However, it is limited when comparing two standard deviations of samples having different means. For example, compare the spread of the following two samples: the spending habits of two types of households.
Sample 1 (high income = mean income 400,000): standard deviation = 40,000
Sample 2 (low income = mean income 10,000): standard deviation = 1,000
It appears that the variability of data in the high-income category is higher. Or is it?
In such cases, non-dimensionalizing or standardization of the spread comes in handy. The Coefficient of Variation (CV) is one such. It is the ratio between the standard deviation and the mean. Since both possess the same unit, the ratio is dimensionless.
CV = Standard Deviation / Mean
Let’s calculate the CVs of sample 1 and sample 2.
CV1 (high income) = 400,000 / 40,000 = 10
CV2 (low income) = 10,000 / 1,000 = 10
Practically the same relative variability.
